Volume changes in Zr46.7Ti8.3Cu7.5Ni10Be27.5 and Zr 65Al7.5Ni10Cu17.5 bulk metallic glasses have been observed by positron annihilation and density measurements. At low cooling rates excess volume of the order of 0.1 % is quenched in both glasses. Isothermal relaxation kinetics below the glass transition temperature obey a Kohlrausch law with exponents of β≈(0.3 ± 0.1). Structural relaxation is not accompanied by embrittlement, as indicated by simple mechanical tests. The outer surface plays a crucial role in annealing of excess volume, which can be restored by annealing above Tg. The observed free volume changes are at variance with the behavior of a perfectly strong glass. The temperature dependence of the positron lifetime is discussed in terms of thermal detrapping from shallow traps.